The value of $a$ for which the system of equations $a^3x + (a + 1)^3y + (a + 2)^3 z = 0$,$ax + (a + 1)y + (a + 2)z = 0$,and $x + y + z = 0$ has a non-zero solution is:

Give the number of electrons in the species $H_{2}^{+}$,$H_{2}$,and $O_{2}^{+}$.

Which of the following alkenes does $NOT$ exhibit $cis-trans$ isomerism?

Which of the following aspects is a defining characteristic of living organisms?

$A$ radioactive nucleus (initial mass number $A$ and atomic number $Z$) emits $3 \,\alpha-$ particles and $2$ positrons. The ratio of the number of neutrons to that of protons in the final nucleus will be:

An infinitely long straight conductor $AB$ is fixed and a current $i_1$ is passed through it. Another movable straight wire $CD$ of finite length carrying current $i_2$ is held perpendicular to it and released. Neglect the weight of the wire.